A372045 - OEIS

A372045

Positions of records in A030000.

0, 7, 11, 22, 50, 61, 78, 100, 121, 122, 127, 155, 263, 548, 1000, 1002, 1003, 1016, 1559, 1583, 1877, 3087, 9634, 10001, 10029, 10199, 10620, 25672, 100002, 100005, 100085, 100116, 100457, 100956, 101597, 101624, 114323, 191974, 1000004, 1000006, 1000055, 1000227, 1000517, 1000717, 1000728, 1027986, 1098714, 1127153, 1429848, 3659369

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

From David A. Corneth, Apr 17 2024: (Start)

0 is a term as it is the least nonnegative integer and A030000(0) = 10.

7 is a term after 0 as 7 is the first number that is first seen at a k such that 2^k contains 7 as a substring (namely at k = 15). (End)

MATHEMATICA

d2k[k_] := d2k[k] = IntegerString[2^k];

A030000[n_] := Block[{d = IntegerString[n], k = -1}, While[StringFreeQ[d2k[++k], d]]; k];